Student, Teach Thyself?

Helping students help themselves

One of my favorite teachers would almost never give me a straight answer. He'd laugh, squint, shake his head…but he wouldn’t bail me out. Steve thought it was crucial for me to come up with the answer myself. If he gave it to me, he’d be robbing me. When I made my own sense out of the material and articulated it successfully, I learned something - something stronger, more flexible, and more useful than any answer a teacher could feed me. 

And I gained confidence. Eventually, I did make sense of it. The more I practiced, the more I started to see a new challenge and think, “I have no idea what this is, but I’m going to figure it out.”

Usually the challenge was music - replicating a segment of Charlie Parker’s “Ornithology” solo, improvising with certain harmonic paths, or maybe creating a categorization of these sounds - but I have carried this approach into my own teaching of math, reading, and writing. I always prefer to let the student discover the answer, often employing the Socratic method up to (and beyond!) the limits of student tolerance. With this approach, the teacher’s role is to create structures that help students learn things on their own.

Students often resist this approach at first: it’s definitely more work for them. And even when they get used to it during sessions, they still resist it on their homework. When you take a test, you shouldn’t just grade it. You should mine the ones you missed: How did I miss that? How would I categorize that error? What could I do next time? But so often, students do not look at questions they’ve missed before we meet. They wait for an explanation. One more example: once you’ve learned something, you should test it again in the future – a couple weeks later, come back to that question you missed and see if you can get it right. But, as I’ve written elsewhere, kids loathe redos.

So one key goal of Mathchops is to help students teach themselves:

• There are no multiple choice options. You have to come up with the answer yourself.

• The explanation is provided immediately after every graded answer… at the moment the student is most motivated to know why they got it wrong.

• The numbers change every time a question appears. You can’t just memorize the answer.

• The topics are mixed. You can’t just focus on one area and memorize it for a short period of time. You have to know it for a long time, and recognize it in many different forms. 

• The questions are right at their level: they’re the ones that a student is missing but could easily get right, or ones they might not have learned but could easily figure out on their own (like the median). If a concept or problem type is within reach, a student is more likely to try to figure it out. 

• Students have a lot of autonomy: betting games, Jeopardy-games, score-raising games, category-specific games. There’s an Analyze page with previous questions, a Create A Quiz page that lets you pick, and a list of starred questions. If students are at all motivated to teach themselves, we try to work with it.

There is still a lot of work for me to do – reviewing the confusing questions, setting goals for next time, relating this work to the real test, motivating the student. But the student does most of the work…and gets the rewards.